Theorem wl-syl5 33247

Description: A syllogism rule of inference. The first premise is used to replace the second antecedent of the second premise. Copy of syl5 34 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
wl-syl5.1	|- ( ph -> ps )
wl-syl5.2	|- ( ch -> ( ps -> th ) )

Assertion

Ref	Expression
wl-syl5	|- ( ch -> ( ph -> th ) )

Proof of Theorem wl-syl5

Step	Hyp	Ref	Expression
1		wl-syl5.2	. 2 |- ( ch -> ( ps -> th ) )
2		wl-syl5.1	. . 3 |- ( ph -> ps )
3	2	wl-imim1i 33245	. 2 |- ( ( ps -> th ) -> ( ph -> th ) )
4	1, 3	wl-syl 33246	1 |- ( ch -> ( ph -> th ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 33241

This theorem is referenced by:  wl-con4i  33249  wl-mpi  33252  wl-ax3  33255  wl-com12  33258  wl-con1i  33260  wl-ja  33261  wl-pm2.04  33267